Determine all possible triplets (A,B,C) of
positive integers such that:
A^{B} + B^{C} = C^{A}
Prove that there are no others.
(In reply to
re: Near Misses by Ady TZIDON)
Indeed
10 for Tot=2 to 9999
20 for A=1 to Tot2
30 for B=A to TotA1
40 C=TotAB
50 if A^B+B^C=C^A then print A;B;C
100 next
110 next
120 next
which checks all A, B and C up to a total of 9999 finds no other solution than 1,1,2 for A,B,C.
Edited on March 9, 2014, 6:55 pm

Posted by Charlie
on 20140309 18:55:13 